Although the piezoelectric effect has been known since the 19th century, the development of quartz crystal devices which oscillate at precisely defined resonant frequencies and which can be incorporated as passive elements into electronic instruments began in the 1920's. Like much of our modern electronic technology, their development received a massive push during World War II, when over 30 million quartz crystal oscillators were produced for use in military communications equipment. Today there is widespread use of quartz crystal oscillators and of newer types of microresonators in electronics wherever precise control of frequency is needed as, for example, in radio frequency communications, in frequency meters and timepieces, in scientific instrumentation, and in computers and cellular telephones.
There are several useful books which describe the physics of quartz crystal oscillators and other microresonators and their use in electronic circuits. For example, Introduction to Quartz Crystal Unit Design by Bottom, Van Nostrand Reinhold, New York, 1982, discusses the physical crystallography of quartz, mechanic vibrations and stress/strain relationships, the piezoelectric effect, the equivalent circuit of the quartz resonator and its use as a circuit component, the temperature stability of quartz oscillators, and other topics of importance in the application of these devices. Science, Vol. 249, pages 1000-1007 (1990), by Ward et al., describes the converse piezoelectric effect and its use in in-situ interfacial mass detection, such as in thickness monitors for thin-film preparation and in chemical sensors for trace gases. Analytical Chemistry, Vol. 65, pages 940A-948A and 987A-996A (1993), by Grate et al., compares the acoustical and electrical properties of five acoustic wave devices used as microsensors and transducers, including quartz crystal oscillators.
Any crystalline solid can undergo mechanical vibrations with minimum energy input at a series of resonant frequencies, determined by the shape and size of the crystal and by its elastic constants. In quartz, such vibrations can be induced by the application of a radio frequency voltage at the mechanical resonant frequency across electrodes attached to the crystal. This is termed the inverse piezoelectric effect. The thickness shear mode is the most common mechanical vibration used in quartz crystal oscillators. A typical commercially available quartz crystal oscillator is a thin circular quartz plate, cut from a single crystal at an angle of 37.25.degree. with respect to the crystal's z axis (the so-called "AT cut"). This angle is chosen so that the temperature coefficient of the change in frequency is, to the first approximation, zero at 25.degree. C., thus minimizing the drift in resonant frequency with ambient temperature change. A slight change in the cut angle produces crystals with zero temperature coefficients at elevated temperatures. The AT-cut plate has thin film electrodes on most of the top and bottom surfaces of the crystal, and is supported in various ways at its circumference or perimeter. Both the fundamental and the first few overtones of the thickness shear mode have been utilized in crystal oscillators. A typical AT-cut quartz disk piezoid operating at a 10.8 MHz fundamental has the following dimensions, according to page 99 of the above-mentioned reference by Bottom:
diameter: 8.0 mm PA1 electrode diameter: 2.5 mm PA1 blank thickness: 0.154 mm
The quality factor, Q, defined for any resonant circuit incorporating quartz crystal oscillators is usually not less than 10.sup.5 and may be as high as 10.sup.7. With careful attention to the control of temperature in a vacuum environment, a short-term frequency stability of one part in 10.sup.10 can be obtained, although the stated short-term stability for commercial units is .+-.3 ppm.
The resonant frequency of a quartz crystal oscillator is inversely proportional to the thickness, e, of the plate. For a circular disk, EQU f=nK/e
where n+1, 3, 5, . . . and K is the frequency constant (for example, see page 134ff of the above-mentioned reference by Bottom). For an AT-cut disk, K 1664 kHz.multidot.mm, so that a disk of a thickness of 1 mm will oscillate at 1.664 MHz. If this thickness is increased by the deposition of material on the surface of the quartz crystal oscillator, then its frequency will decrease.
In 1957, Sauerbrey in Z. Physik, Vol. 155, 206 (1959), derived the fractional decrease in frequency .DELTA.f of a circular disk quartz crystal oscillator upon deposition of a mass, .DELTA.m, of material on its surface. The derivation relies on the assumption that a deposited foreign material exists entirely at the anti-node of the standing wave propagating across the thickness of the quartz crystal, so that the foreign deposit can be treated as an extension of the crystal, as, for example, described in Applications of Piezoelectric Quartz Crystal Microbalances by Lu et al., Elsevier, New York, 1984. Sauerbrey's result for the fundamental vibrational mode is as follows: EQU .DELTA.f/f.sub.0 =-.DELTA.e/e.sub.0 =-2f.sub.0 m/A.rho..mu.
Here, .DELTA.e is the change in the original thickness e.sub.o, A is the piezoelectrically active area, p is the density of quartz, and .mu. is the shear modulus of quartz. By measuring the decrease in frequency, one thus can determine the mass of material deposited on the crystal. This is the principle of the quartz crystal microbalance. In practice, the assumptions underlying the Sauerbrey equation are valid for deposits up to 10% of the crystal mass, although the sensitivity to mass has been shown experimentally to decrease from the center of the electrode to its edge.
Torres et al. in J. Chem. Ed., Vol. 72, pages 67-70 (1995), describe the use of a quartz crystal microbalance to measure the mass effusing from Knudsen effusion cells at varying temperatures, in order to determine the enthalpies of sublimation. They reported a sensitivity of about 10.sup.-8 g/sec in the mass deposition rate. The application of the quartz crystal microbalance and other microresonators in chemistry for the sensitive detection of gases adsorbed on solid absorbing surfaces has been reviewed by Alder et al., in Analyst, Vol. 108, pages 1169-1189 (1983) and by McCallum in Analyst, Vol. 114, pages 1173-1189 (1989). The quartz crystal microbalance principle has been applied to the development of thickness monitors in the production of thin films by vacuum evaporation, as, for example, described in the above-mentioned reference by Lu et al. Quartz crystal oscillators of various sizes and modes of vibration are commonly used currently in research efforts in sensor development.
Throughout this application, various publications and patents are referred to by an identifying citation. The disclosures of the publications and patents referenced in this application are hereby incorporated by reference into the present disclosure to more fully describe the state of the art to which this invention pertains.
U.S. Pat. No. 5,339,051 to Koehler et al. describes resonator-oscillators for use as sensors in a variety of applications. U.S. Pat. No. 4,596,697 to Ballato and U.S. Pat. No. 5,151,110 to Bein et al. describe coated resonators for use as chemical sensors.
To overcome the influences of temperature changes on the microresonators, U.S. Pat. No. 4,561,286 to Sekler et al. and U.S. Pat. No. 5,476,002 to Bower et al. describe active temperature control or the use of temperature sensors with the microresonators. U.S. Pat. No. 5,686,779 to Vig describes a microresonator for direct use as a thermal sensor.
Microresonators, including quartz crystal microbalances (QCM's), have been utilized to determine the mass changes with a variety of liquid samples such as, for example, described in U.S. Pat. No. 4,788,466 to Paul et al. When the microresonator is coated, chemicals present in the liquid samples may be detected as, for example, described in U.S. Pat. No. 5,306,644 to Myerholtz et al.
Microresonators have been adapted to measure the viscosity of a liquid sample as, for example, described in U.S. Pat. No. 4,741,200 to Hammerle. U.S. Pat. No. 5,201,215 to Granstaff et al. describes the use of microresonators to measure the mass of a solid and physical properties of a fluid in a sample.
Calorimeters for various types of heat measurements are well known as, for example, described in U.S. Pat. No. 4,492,480 to Wadso et al.; U.S. Pat. No. 5,295,745 to Cassettari et al.; and U.S. Pat. No. 5,312,587 to Templer et al. A combined scientific apparatus of a thermal analyzer, such as a calorimeter, and an X-ray diffractometer for observing simultaneously both thermodynamic and structural properties of materials is described in U.S. Pat. No. 4,821,303 to Fawcett et al.
Despite the various approaches proposed for the design of sensors based on microresonators as the sampling device, there remains a need for sensors which can simultaneously and continuously measure with high sensitivity and accuracy both mass and heat flow changes of a sample in contact with the microresonator.